Balancing parallel robots throughout their workspace while avoiding the use of balancing masses and respecting design practicality constraints is difficult. Medical robots demand such compact and lightweight designs. This paper considers the difficult task of achieving optimal approximate balancing of a parallel robot throughout a desired task-based dexterous workspace using balancing springs only. While it is possible to achieve perfect balancing in a path, only approximate balancing may be achieved without the addition of balancing masses. Design considerations for optimal robot base placement and the effects of placement of torsional balancing springs are presented. Using a modal representation for the balancing torque requirements, we use recent results on the design of wire-wrapped cam mechanisms to achieve balancing throughout a task-based workspace. A simulation study shows that robot base placement can have a detrimental effect on the attainability of a practical design solution for static balancing. We also show that optimal balancing using torsional springs is best achieved when all springs are at the actuated joints and that the wire-wrapped cam design can significantly improve the performance of static balancing. The methodology presented in this paper provides practical design solutions that yield simple, lightweight and compact designs suitable for medical applications where such traits are paramount.